Brains perform decision-making by Bayes theorem. The theorem quantifies events as probabilities and, based on probability rules, renders the decisions. Learning from this, Bayes theorem can be applied to enable efficient user-scene interactions. However, given the probabilistic nature, implementing Bayes theorem in hardware using conventional deterministic computing can incur excessive computational cost and decision latency. Though challenging, here we present a probabilistic computing approach based on memristors to implement the Bayes theorem. We integrate memristors with Boolean logics and, by exploiting the volatile stochastic switching of the memristors, realise probabilistic logic operations, key for hardware Bayes theorem implementation. To empirically validate the efficacy of the hardware Bayes theorem in user-scene interactions, we develop lightweight Bayesian inference and fusion hardware operators using the probabilistic logics and apply the operators in road scene parsing for self-driving, including route planning and obstacle detection. The results show our operators can achieve reliable decisions in less than 0.4 ms (or equivalently 2,500 fps), outperforming human decision-making and the existing driving assistance systems.